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2 Answers
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Im pretty happy with my nVidia GeForce 9600 GT Silent Edition. It´s very quiet (off course, its only cooled passively) and it´s got dual DVI output. Here is a link to the homepage of nVidia for detailled specification. I don´t say, that you should buy THIS card especially. But I do say, that there is a Silent Edition to most of the nVidia Models. But to be fair, here is also a link to the ATI page. I dont want to make special advertisement. So you should especially know, what you want.
So the best thing to do is read some tests from reliable sources about the different cards after getting a quick overview on the market.

Because of this information:

(I will be using the machine mostly for work, so don't want it burning through the electricity bill)

I assume, a Grafics card in the performance of my card would be enough.

Low power (I will be using the machine mostly for work, so don't want it burning through the electricity bill)

Good performance (however, I would be nice to play to odd game from time to time)

Dual DVI output.

Not too expensive

With the exception of dual DVI output, every other criteria is fairly relative.

How quiet?
What do you concider low power?
What games?
what price range?

The 9600 GT is a good card for the price ($80 -$100) & does have duel DVI & of course Nvidia has the PhysX driver, but I am a Radeon fan myself. (person choice) The Radeon HD 4670 compares to the 9600 in benchmarks & cost about the same, although it's kind of difficult to find one with DUAL DVI. Most Radeon cards in the 4XXX series have 1) DVI, 1) HDMI & 1) standard VGA but thats what adapters are for.

For a few extra dollars you could bump up to the XFX Radeon 4770 which will give much better graphics performance but use a lot more power.

Personally, if my assumption of your situation is correct, I'd go with the Radeon HD4350 & a VGA to DVI adapter.

MSI makes a great card (I use it myself in one of my computers) that states it's required power is 300W. I've use a 250W for over a year without any issues at all. I've played COD Modern Warfare 1 & 2, Fallout 3, Farcry 2, GTA IV, & Crysis.

Radeon's Catalyst Control Center has a build in overclock utility which with one click will find the max capability of your system & push it to it's limit without any danger to hardware or software. I went from 6 Frames Per Second (Crysis) to 12FPS. Playing Crysis at 12FPS doesn't sound like very much fun but it works at low setting, looks good, runs well & for a $30 card in a stock computer it's pretty darn good investment to me.